Write the equation of a line that is parallel to ${y=-7}$ and that passes through the point ${(7,5)}$.
Answer: Getting started Key idea: Parallel lines have the same slope. Step 1: Find the slope Where is the slope? There is no $x$ -term in the equation, so $x$ has a coefficient of $0$. The slope of the given line: ${0}$ Slope of the parallel line: $C{0}$ Step 2: Substitute the known point into linear equation The parallel line will have a slope of $C{0}$ and pass through the point ${(7,5)}$. Let's start from the point-slope form of the equation of the parallel line, then solve for $y$. [What is the point-slope form?] $\begin{aligned} y-{5} &= C{0}(x-{7})\\\\\\ y -5&= 0\\\\ y&={5} \end{aligned}$ Answer The equation of the parallel line is $y = {5}$. ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ ${2}$ ${4}$ ${6}$ ${8}$ ${\llap{-}4}$ ${\llap{-}6}$ ${\llap{-}8}$ $y$ $x$